Complete radiation boundary conditions for the Helmholtz equation II: domains with corners

This paper continues Part I (Hagstrom and Kim in Numer Math 141(4):917–966, 2019) of the investigation on the complete radiation boundary condition (CRBC) in waveguides. In this paper, we propose corner compatibility conditions for CRBC applied to the Helmholtz equation posed in R². Since CRBC is developed as a high-order absorbing boundary condition approximating the radiation condition by using rational functions via the cross-sectional Fourier analysis, it is well-studied and its accurate performance is validated on a straight/planar fictitious boundary in waveguides. However in the presence of corners on artificial absorbing boundaries such as boundaries of rectangular domains, a special treatment for corner conditions is required. We design and validate the accurate CRBC with the corner compatibility conditions on rectangular domains. We also analyze the existence and uniqueness of solutions to the Helmholtz equation coupled with CRBC with the corner compatibility conditions. Finally, numerical experiments illustrating the accuracy of CRBC will be presented.